is fulfilled for the matrix \(Y_{f}(t):=Y_f(q(t),\dot{q}(t),q_f(t)) \in \mathbb {R}^{4\times 9}\)  defined in (REF ) for some \(T>0\)  and \(\lambda _{z}>0\) , then it can be shown using the standard arguments of adaptive control for a linearly parametrized uncertainty (e.g., [1]})
that the set \(\lbrace  \zeta _{2}\in \mathcal {X}_{2} | e= 0_{4\times 1}, \eta _{1}=0_{4\times 1}, \tilde{\Theta } = 0_{9\times 1} \rbrace \)  is globally exponentially stable.
